## Algebra and its Applications |

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### Contents

The Jacobian Conjecture | 1 |

3 Symbolic Powers and Number of Defining Equations C Cowsik | 13 |

NonFree Projective Ideals of HXY and Quadratic | 41 |

Copyright | |

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abelian group associated automorphisms Boolean Boolean-like ring C*-algebras characterization commutative completely condition contains Corollary corresponding defined denote Department of Mathematics digraph domain Dutta Majumder element epimorphism equations equivalent exists factorized finite group finitely generated projective free group functions fuzzy set graph group algebra group G group rings Hence homomorphism idempotent implies India induced integral inverse isomorphic k-cycle KQ(R lattice ordered Lemma Let G Lie algebra linear Markoff Math matrix maximal character maximal ideal minimal multiplication near-ring nilpotent noetherian nonnegative matrices nonzero operators order-unit ordered abelian groups p-abelian p-group partially ordered abelian permutation matrix polynomial prime ideal Proc projective modules Proof properties Proposition proved PVMD quotient R-module rank regular ring representable autometrized algebra result S-matrix satisfies semigroup sequence solution solvable structure submodule subset Suppose symmetric t-ideal ta-matrix Theorem 2.3 theory tion topology ultramatricial unique University vector X-chains zero divisors